Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
356 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #89863 | C2 | semidirect |
| 4. #89850 | C2 | semidirect |
| 5. #89823 | C2 | semidirect |
| 6. #89816 | C2 | semidirect |
| 7. C4×#1144 | C2 | semidirect |
| 8. #89793 | C2 | semidirect |
| 10. #89742 | C2 | semidirect |
| 11. C2×#6381 | C2 | semidirect |
| 89. C7×D4 | Q16 | semidirect |
| 197. D4 | #1144 | semidirect |
| 215. C7 | #3338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#554 | 2 |
| #90234 | 2 |
| #89863 | 2 |
| #89850 | 2 |
| #89823 | 2 |
| #89816 | 2 |
| C4×#1144 | 2 |
| #89793 | 2 |
| D4×C7⋊C8 | 2 |
| #89742 | 2 |
| C2×#6381 | 2 |
| #3338 | 7 |